The invention concerns a magnetic resonance method for using radio frequency pulses for spatially selective and frequency selective or multidimensionally spatially selective excitation of an ensemble of nuclear spins having an initial distribution of magnetization in a main magnetic field aligned along a z-axis, wherein a spin magnetization with a given target distribution of magnetization is generated, and for a correspondingly selective refocusing of the spin magnetization. Such a method is known from [4].
Use of radio frequency (=RF) pulses generated by RF coils in conjunction with magnetic field gradients is the standard slice selection method in magnetic resonance imaging, wherein the gradients are temporally constant and the RF pulses have a sinc(t)-like envelope. This method can be understood as excitation along a k-space line.
Multidimensional spatial selection therefore requires passing through k-space in the appropriate dimensionality during excitation, which has so far been extremely difficult to do in feasible time (<20 ms) due to slew-related limitations (hardware and nerve stimulation). The emergence of parallel excitation techniques, however, has allowed the pulse duration to be shortened during excitation by using several spatially inhomogeneous emitting coils, and spatially selective excitation and refocusing in 2 and 3 dimensions or in conjunction with a frequency dimension are becoming feasible. [1] demonstrates first experimental configurations and shows the state of the art in the small angle region.
Spatially selective excitation in several dimensions is designed for applications such as inner volume imaging, outer volume saturation or spectroscopy, wherein an arbitrary (anatomically) formed region of the sample/the test person (target sample) is selected and only that particular region is excited or refocused. This type of selective excitation therefore requires specific calculation of RF pulses for each target sample. Furthermore, the emitting profiles of the RF coils are specific for each patient, so the RF pulses additionally depend on the measured emitting profiles, which are only available when the patient is already in the tomograph. Consequently, a highly important criterion for the applicability of anatomically adjusted spatially selective excitation in addition to the accuracy of the excitation pattern is the time needed to calculate the RF pulses.
The Bloch Equations describe the time dependent distribution of spin magnetization M in the fields B0 (main magnetic field), B1 (radio frequency field) and magnetic field gradients G as follows (letters in bold print represent vectorial values):
                                          ∂                          ∂              t                                ⁢          M                =                              (                                                            0                                                                      Δ                    ⁢                                                                                  ⁢                    ω                                                                                                              -                      γ                                        ⁢                                                                                  ⁢                                          B                                              1                        ,                        x                                                                                                                                                                                    -                      Δ                                        ⁢                                                                                  ⁢                    ω                                                                    0                                                                      γ                    ⁢                                                                                  ⁢                                          B                                              1                        ,                        y                                                                                                                                                              γ                    ⁢                                                                                  ⁢                                          B                                              1                        ,                        x                                                                                                                                                        -                      γ                                        ⁢                                                                                  ⁢                                          B                                              1                        ,                        y                                                                                                              0                                                      )                    ⁢          M                                    (        1        )            wherein M, B1 and Δω are position and time dependent. The following applies to an isochromate: Δω(t, r)=y[r·G(t)−ΔB0(r)], wherein the spatially varying off-resonance term ΔB0(r) describes inhomogeneities in the main magnetic field. T1 and T2 relaxation are neglected here.
For the purpose of multidimensionally selective excitation, the Bloch Equations in form (1) are regarded as a discretized system of differential equations with Ns (number of points at which the target distribution of magnetization is given (grid points)) vector equations and with Nc (number of RF coils) multiplied by Nt (number of time increments) degrees of freedom to determine the RF pulses II(t) associated with the field B1 via the emitting profiles of the coils.
Two main approaches to solving this system of equations are described in literature:    1. Optimal control [2,3], which provides high accuracy of the excitation pattern. This approach is based on solving the system of equations (1) using methods of variational calculus and requires a complete forward solution (integration) of the Bloch Equations per RF optimization step (iteration) to determine the excitation error and a complete backward integration to obtain the RF pulse optimized by one step. This method is exact but, with typical calculation times of up to 15 minutes on state-of-the-art computers, too time-consuming and CPU-intensive for a feasible solution. It is therefore not suited for use in clinical routines where the fastest method with appropriate accuracy must be chosen.    2. Transmit SENSE [1,4,5] (in small tip angle approximation), which is based on approximation of the Bloch Equations for small tip angles. This approximation reduces solving the Bloch Equations to solving a linear equation in II (RF amplitude and phase of the I-st coil) for transverse magnetization Mt:
                                          M            t                    ⁡                      (            r            )                          =                  ⅈ          ⁢                                          ⁢          γ          ⁢                                          ⁢                                    M              0                        ⁡                          (              r              )                                ⁢                                    ∫              0              T                        ⁢                                                  ⁢                                          ⅆ                t                            ⁢                                                ∑                  l                                ⁢                                                                            S                      l                                        ⁡                                          (                      r                      )                                                        ⁢                                                            I                      l                                        ⁡                                          (                      t                      )                                                        ⁢                                      exp                    ⁡                                          [                                              ⅈ                        ⁡                                                  (                                                                                                                    k                                ⁡                                                                  (                                  t                                  )                                                                                            ·                              r                                                        +                                                          Δ                              ⁢                                                                                                                          ⁢                                                                                                ω                                  0                                                                ⁡                                                                  (                                  r                                  )                                                                                            ⁢                                                              (                                                                  T                                  -                                  t                                                                )                                                                                                              )                                                                    ]                                                                                                                              (        2        )            wherein SI represent the emitting profiles of the RF coils, T represents the total duration of the RF pulse, M0 represents the magnetization toward the z-axis at the onset of the pulse (t=0), k(t) represents the k-space trajectory resulting from the course of the gradients G(t), and Δω0(r) represents the off resonance resulting from the inhomogeneity of the B0 field. The emitting profiles, the transverse magnetization and the RF are complex quantities: each of the x-components is represented by the real part and each of the y-components by the imaginary part.
The linearity of this remaining problem and the fact that the equations decouple for the z-components of the magnetization, allow relatively quick and simple calculation of the RF pulses. The inherent small angle approximation, however, rules out exclusive use of this method of calculation for pulses with large tip angles >15°, which are indispensable for efficient excitation of the spin magnetization and for all spin-echo-based sequences.
The present invention is based on the task of improving a method of the kind described in the introduction so as to help avoid the disadvantages described above.